https://www.scipedia.com/wd/index.php?action=history&feed=atom&title=Berzins_2021aBerzins 2021a - Revision history2026-04-24T13:56:06ZRevision history for this page on the wikiMediaWiki 1.27.0-wmf.10https://www.scipedia.com/wd/index.php?title=Berzins_2021a&diff=218924&oldid=prevScipediacontent: Scipediacontent moved page Draft Content 867464886 to Berzins 2021a2021-03-11T15:54:23Z<p>Scipediacontent moved page <a href="/public/Draft_Content_867464886" class="mw-redirect" title="Draft Content 867464886">Draft Content 867464886</a> to <a href="/public/Berzins_2021a" title="Berzins 2021a">Berzins 2021a</a></p>
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</td></tr></table>Scipediacontenthttps://www.scipedia.com/wd/index.php?title=Berzins_2021a&diff=218923&oldid=prevScipediacontent: Created page with "== Abstract == The provision of appropriate time integration methods for the Material Point Method (MPM) involves considering stability, accuracy and energy conservation. A c..."2021-03-11T15:54:20Z<p>Created page with "== Abstract == The provision of appropriate time integration methods for the Material Point Method (MPM) involves considering stability, accuracy and energy conservation. A c..."</p>
<p><b>New page</b></p><div>== Abstract ==<br />
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The provision of appropriate time integration methods for the Material Point Method (MPM) involves considering stability, accuracy and energy conservation. A class of methods that addresses many of these issues are the widely-used symplectic time integration methods. Such methods have good conservation properties and have the potential to achieve high accuracy. In this work we build on the work in [5] and consider high order methods for the time integration of the Material Point Method. The results of practical experiments show that while high order methods in both space and time have good accuracy initially, unless the problem has relatively little particle movement then the accuracy of the methods for later time is closer to that of low order methods. A theoretical analysis explains these results as being similar to the stage error found in Runge Kutta methods, though in this case the stage error arises from the MPM differentiations and interpolations from particles to grid and back again, particularly in cases in which there are many grid crossings.<br />
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== Full document ==<br />
<pdf>Media:Draft_Content_867464886p1127.pdf</pdf></div>Scipediacontent